New Delhi, April 4 -- Until quite recently, the prevailing image to outsiders of The Church of Jesus Christ of Latter-day Saints has been male missionaries wearing white shirts and name tags, evoked by the hit Broadway show "The Book of Mormon."

But another unofficial face of the male-led church has emerged in American pop culture: digitally savvy, female influencers, often seen sporting athleisure, a giant soda in hand - and varying degrees of adherence to church teachings.

These influencers have found an enthusiastic audience across the country, curious about their faith and families. Some explain the tenets of what's widely known as the Mormon church, but others bring attention to the rules they often break - drinking alcohol, having...